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I really hate questions like this. Since they mistake rationality for computer-like adherence to a set of rules. —————————————————————— Imagine a 100 rounds o

I really hate questions like this. Since they mistake rationality for computer-like adherence to a set of rules. —————————————————————— Imagine a 100 rounds of ultimatum games. In each round, Alice proposes a split of $1 and Bob can either accept or reject. If Bob rejects, the $1 is burned in a fire. How much money will each end up with? Lets work backwards, as we do in the pirate game. In ROUND100, Alice knows Bob will take whatever non-zero offer she makes. She can offer him 1 cent and Bob will agree. In ROUND99, Alice knows that Bob can will accept whatever non-zero offer she makes in ROUND100, so she can make whatever non-zero offer she wants this round without fear of repercussion. She offers him 1 cent and knows he will agree. Continuing to work backwards, we find that in all 100 rounds, Alice takes 99 cents and offers Bob 1 cent. Alice ends up with $99 and Bob ends up with $1. —————————————————————— This is obviously (and experimentally proven) not what would happen in real life. In experimental outcomes, Bob rejects offers that are too low to broadcast that he is “irrational”. As a result, Bob is able to negotiate a much higher outcome (around 40%). So who is more rational? The "rational" Bob who gets $1, or the “irrational” Bob who gets $40?

robzyb 11y ago
I really love questions like this. The insight obtained from from comparing the computer-like rationality to what would happen in the real world is truly fascinating to me. Also, your example of Bob negotiating fits in very well with the theoretical computer-like rationality. Alice's offer of 1c is equivalent to an offer of 0c nominal in the hypothetical case. The real-life 40% is more a commentary of utility of money as opposed to decision making. I think that you're conflating concepts.
- aakilfernandes 11y ago
  I should rephrase. I hate it from an interview-question point of view. I like it from an insight point of view.
- resu_nimda 11y ago
  What are some such insights to be gained from the pirate example? What did we learn? How a set of "rational" computers might play out this scenario? How do we apply that to our decision making? These questions might seem obtuse or questioning the value of game theory, but I'm just having a hard time understanding what to take from it. The real-life 40% is more a commentary of utility of money as opposed to decision making. Only real-life humans make decisions though. If there is no implied utility of money then Bob might as well reject all offers. And it does seem that the only important question is "what would real humans do?" We can set up a simulation that strictly adheres to a simple set of rules and watch how it plays out, but what is that telling us?
  - bduerst 11y ago
    Game theory is often used as a guiding principle in human negotiations, but as you say, there is never a truly isolated system when it comes to people in real world situations. Good negotiators are cognizant of this.
  - the_af 11y ago
    > What are some such insights to be gained from the pirate example? What did we learn? It's a logic puzzle. We learned that the intuitive solution of having the first proposal be "I don't want any money, I just want to live" is too conservative, and that there is a way better solution for the first pirate. We didn't gain any deep insight in how to split money between real people, since those cases seldom involve pure, unemotional logic.
- Dr_tldr 11y ago
  I think what game theory could use is a little bit of the concept of price-of-entry into a new market, Ie, doing something at a loss now in order to generate profit later. This is similar but not exactly the same as the idea of a loss-leader. What a lot of classic game theory is missing is the idea of a feedback-loop. In a game where "Bob" is continually offered one cent, if he burns the other player who is trying to get the other 99 cents, he's signaling that they'll have to cut him a better deal. The other player would be irrational to continue offering the 99/1 split after it had been previously rejected. For the other player, even (especially!) if it's a computer, the rational choice is to keep upping Bob's percentage until it finds a number he'll accept. So you're right that 40% only speaks to a specific utility, but in any case, the only rational number is whatever number Bob (and the first player) will accept.
JupiterMoon 11y ago
> mistake rationality for computer-like adherence to a set of rules I might be mistaken but I think in terms of economics that this is literally the definition of rationality. Your experimental example is with real people. Real people are not rational actors (as a rational actor is defined in economics). This is considered by many to be a major flaw in traditional economics.
- aakilfernandes 11y ago
  By the definition I understand, rational means payoff maximizing. How an actor gets to payoff maximization is irrelevant. In other words if "irrational" actions result in payoff maximization, then the "irrational" actions ARE rational.
- danmaz74 11y ago
  > Real people are not rational actors (as a rational actor is defined in economics). This is considered by many to be a major flaw in traditional economics. On the flip side, this is considered by many traditional economists to be a major flaw in real people.
  - aakilfernandes 11y ago
    Seeing as the "irrational" actor outperforms the "rational" actor, we should be happy real people are "irrational" at least some of the time.
    - boxy310 11y ago
      This is probably because evolution operates on a genetic systematic basis, rewarded by external outputs. Capacity for rational thought is a side effect of this process, and does not necessarily proceed from first principles like much of economics would prefer.
      - JupiterMoon 11y ago
        I.e. classical rational economics is wrong -- and you provide a first principle reason why (adding to the experimental stuff I already knew about).
Perceval 11y ago
https://en.wikipedia.org/wiki/Madman_theory https://en.wikipedia.org/wiki/Madman_theory
CPLX 11y ago
This 100 round progression reminds me of (though is not equivalent to) Zeno's Paradox.
Kapow 11y ago
>In ROUND100, Alice knows Bob will take whatever non-zero offer she makes. Wait, how does she know that? Can you explain why you consider that the most rational choice for Bob to make? As experiment shows, this is not the optimal strategy, so I don't see why you would call it the "rational" one. Also, keep in mind that you're describing an iterative game (where the same people play the same game with the same circumstances repeatedly) and the pirate game is non-iterative, since the players and circumstances change between rounds. As you note, iterative games are much more complicated and the sort of induction used in the pirate game doesn't really work.
- ultramancool 11y ago
  > As experiment shows, this is not the optimal strategy, so I don't see why you would call it the "rational" one. It's rational because if Bob accepts an offer for a positive value of money, even if it's a cent, he gains value from it. Rejecting it just throws that cent away, which he could have had in his pocket, it's irrational to throw away this value. There's a difference between rational and optimal for a reason though, but you need to feel like you're getting ripped off for that to come into play, you need to feel like you'd rather someone else lose $0.99 than you gain $0.01.
  - Kapow 11y ago
    That only makes sense if you restrict Bob's decision making to consider each game in isolation, without regard to how how rejecting an offer in one game might lead to a higher offer in a future game. At that point, I would call it a different problem entirely, so there isn't much point in comparing the results. I certainly wouldn't label that version of the problem "rational" and the version where Bob considers future games "irrational".
  - Tyr42 11y ago
    But pre-commiting to a strategy of say: "accept if 40 cents or more" could net more coins overall, right? I agree that if it was a one off game, then that would make sense, but it's an iterated game.

robzyb 11y ago

I really love questions like this. The insight obtained from from comparing the computer-like rationality to what would happen in the real world is truly fascinating to me. Also, your example of Bob negotiating fits in very well with the theoretical computer-like rationality. Alice's offer of 1c is equivalent to an offer of 0c nominal in the hypothetical case. The real-life 40% is more a commentary of utility of money as opposed to decision making. I think that you're conflating concepts.

aakilfernandes 11y ago
I should rephrase. I hate it from an interview-question point of view. I like it from an insight point of view.
resu_nimda 11y ago
What are some such insights to be gained from the pirate example? What did we learn? How a set of "rational" computers might play out this scenario? How do we apply that to our decision making? These questions might seem obtuse or questioning the value of game theory, but I'm just having a hard time understanding what to take from it. The real-life 40% is more a commentary of utility of money as opposed to decision making. Only real-life humans make decisions though. If there is no implied utility of money then Bob might as well reject all offers. And it does seem that the only important question is "what would real humans do?" We can set up a simulation that strictly adheres to a simple set of rules and watch how it plays out, but what is that telling us?
- bduerst 11y ago
  Game theory is often used as a guiding principle in human negotiations, but as you say, there is never a truly isolated system when it comes to people in real world situations. Good negotiators are cognizant of this.
- the_af 11y ago
  > What are some such insights to be gained from the pirate example? What did we learn? It's a logic puzzle. We learned that the intuitive solution of having the first proposal be "I don't want any money, I just want to live" is too conservative, and that there is a way better solution for the first pirate. We didn't gain any deep insight in how to split money between real people, since those cases seldom involve pure, unemotional logic.
Dr_tldr 11y ago
I think what game theory could use is a little bit of the concept of price-of-entry into a new market, Ie, doing something at a loss now in order to generate profit later. This is similar but not exactly the same as the idea of a loss-leader. What a lot of classic game theory is missing is the idea of a feedback-loop. In a game where "Bob" is continually offered one cent, if he burns the other player who is trying to get the other 99 cents, he's signaling that they'll have to cut him a better deal. The other player would be irrational to continue offering the 99/1 split after it had been previously rejected. For the other player, even (especially!) if it's a computer, the rational choice is to keep upping Bob's percentage until it finds a number he'll accept. So you're right that 40% only speaks to a specific utility, but in any case, the only rational number is whatever number Bob (and the first player) will accept.

JupiterMoon 11y ago

> mistake rationality for computer-like adherence to a set of rules I might be mistaken but I think in terms of economics that this is literally the definition of rationality. Your experimental example is with real people. Real people are not rational actors (as a rational actor is defined in economics). This is considered by many to be a major flaw in traditional economics.

aakilfernandes 11y ago
By the definition I understand, rational means payoff maximizing. How an actor gets to payoff maximization is irrelevant. In other words if "irrational" actions result in payoff maximization, then the "irrational" actions ARE rational.
danmaz74 11y ago
> Real people are not rational actors (as a rational actor is defined in economics). This is considered by many to be a major flaw in traditional economics. On the flip side, this is considered by many traditional economists to be a major flaw in real people.
- aakilfernandes 11y ago
  Seeing as the "irrational" actor outperforms the "rational" actor, we should be happy real people are "irrational" at least some of the time.
  - boxy310 11y ago
    This is probably because evolution operates on a genetic systematic basis, rewarded by external outputs. Capacity for rational thought is a side effect of this process, and does not necessarily proceed from first principles like much of economics would prefer.
    - JupiterMoon 11y ago
      I.e. classical rational economics is wrong -- and you provide a first principle reason why (adding to the experimental stuff I already knew about).

Perceval 11y ago

https://en.wikipedia.org/wiki/Madman_theory https://en.wikipedia.org/wiki/Madman_theory

CPLX 11y ago

This 100 round progression reminds me of (though is not equivalent to) Zeno's Paradox.

Kapow 11y ago

>In ROUND100, Alice knows Bob will take whatever non-zero offer she makes. Wait, how does she know that? Can you explain why you consider that the most rational choice for Bob to make? As experiment shows, this is not the optimal strategy, so I don't see why you would call it the "rational" one. Also, keep in mind that you're describing an iterative game (where the same people play the same game with the same circumstances repeatedly) and the pirate game is non-iterative, since the players and circumstances change between rounds. As you note, iterative games are much more complicated and the sort of induction used in the pirate game doesn't really work.

ultramancool 11y ago
> As experiment shows, this is not the optimal strategy, so I don't see why you would call it the "rational" one. It's rational because if Bob accepts an offer for a positive value of money, even if it's a cent, he gains value from it. Rejecting it just throws that cent away, which he could have had in his pocket, it's irrational to throw away this value. There's a difference between rational and optimal for a reason though, but you need to feel like you're getting ripped off for that to come into play, you need to feel like you'd rather someone else lose $0.99 than you gain $0.01.
- Kapow 11y ago
  That only makes sense if you restrict Bob's decision making to consider each game in isolation, without regard to how how rejecting an offer in one game might lead to a higher offer in a future game. At that point, I would call it a different problem entirely, so there isn't much point in comparing the results. I certainly wouldn't label that version of the problem "rational" and the version where Bob considers future games "irrational".
- Tyr42 11y ago
  But pre-commiting to a strategy of say: "accept if 40 cents or more" could net more coins overall, right? I agree that if it was a one off game, then that would make sense, but it's an iterated game.